the dot plot shows the number of hours, rounded to the nearest half hour, it took alexis to box braid the…

the dot plot shows the number of hours, rounded to the nearest half hour, it took alexis to box braid the hair of 30 customers. alexis says that the mean time is greater than 7 hours. is she correct? use the drop - down menus to explain. box braids time (h) click the arrows to choose an answer from each menu. the data in the dot plot are choose... and have a median of choose... hours. based on the shape of the data, the mean time will be choose... the median time. therefore, alexis is choose... .

the dot plot shows the number of hours, rounded to the nearest half hour, it took alexis to box braid the hair of 30 customers. alexis says that the mean time is greater than 7 hours. is she correct? use the drop - down menus to explain. box braids time (h) click the arrows to choose an answer from each menu. the data in the dot plot are choose... and have a median of choose... hours. based on the shape of the data, the mean time will be choose... the median time. therefore, alexis is choose... .

Answer

Explanation:

Step1: Count data - point frequencies

There are 2 points at 2.5, 2 at 3, 1 at 3.5, 5 at 4.5, 7 at 5.5, 8 at 6.5, 4 at 7.5, 1 at 8.5, 1 at 9.5. Total number of data - points (n = 30).

Step2: Find the median

Since (n = 30) (an even - numbered data set), the median is the average of the 15th and 16th ordered data - points. Counting the frequencies, the 15th and 16th ordered data - points fall in the 6.5 category. So the median is 6.5 hours.

Step3: Calculate the mean

[ \begin{align*} \bar{x}&=\frac{2\times2.5 + 2\times3+1\times3.5 + 5\times4.5+7\times5.5 + 8\times6.5+4\times7.5+1\times8.5+1\times9.5}{30}\ &=\frac{5 + 6+3.5 + 22.5+38.5 + 52+30+8.5+9.5}{30}\ &=\frac{175}{30}\approx5.83 \end{align*} ]

Step4: Compare mean and median

The mean ((\approx5.83)) is less than the median (6.5). And the mean is less than 7.

Answer:

The data in the dot - plot are symmetric and have a median of 6.5 hours. Based on the shape of the data, the mean time will be less than the median time. Therefore, Alexis is incorrect.